There are only 2 sorts of applicants in the UK
1)Home/EU - parents have paid taxes (usually income taxes) in an EU country for at least the last 3 years. These students are entitled to reduced fees.
2) Everyone else who pays the full fees.
It has nothing to do with nationality. It sounds like you fall into the second group and no passport will change this.
There is one common application form at UCAS UCAS - Home
You can only apply to a maximum of 5 schools through UCAS and you cannot apply to both Oxford and Cambridge in the same year for undergraduate.
Admission to Oxbridge is based on grades and an interview at least. For some subjects you may be asked to submit written work in advance, and for others there are additional exams.
You have to apply for a specific subject or course. This is effectively your major. It is extremely difficult to switch course once admitted, short of dropping out and re-applying.
ECs are in general irrelevant for admission unless specifically related to your course. eg if you apply to study English, if you have edited the school newspaper, you could mention this in the personal statement of the UCAS form (briefly).
If you look on the Oxford and Cambridge websites, look at the courses you are interested in studying and see what A-levels subjects are recommended for admission. You need to take SATs/APs in these subjects, at least 5-6 of them, to have a realistic chance of admission.
The application deadline is usually around 15th October the year before admission (eg for October 2012 admission the application deadline is 15 October 2011).
Many (but not all) US undergraduates who are successfully admitted to Oxbridge have already completed a year at a US college first.
There is more but you are very early to be thinking about this and I think these are the main points. I guess you probably have family in the UK so possibly you will be able to visit Oxford and/or Cambridge before you apply (or maybe you have already visited?). They run open days for prospective students in the summer so if you can go to one of these, I would take that opportunity.